Beta-eta-complete models for System F
Résumé
We show that Friedman's proof of the existence of non-trivial beta-eta-complete models of the simply typed lambda-calculus can be extended to System F. We isolate a set of conditions which are sufficient to ensure beta-eta-completeness for a model of F (and alpha-completeness at the level of types), and we discuss which class of models we get. In particular, the model introduced by Barbanera and Berardi, having as polymorphic maps exactly all possible Scott continuous maps, is beta-eta-complete and hence is the first known complete nonsyntactical model of F. In order to have a suitable framework in which to express the conditions and develop the proof, we also introduce the very natural notion of "polymax models" of System F.